This is a markdown cell

Here is a math expression \[ x+1 = 0 \]

Here is a more complex

\[ x^2_0 + y_1 = 0 \]

Here is how you exert greater control over the sub and superscripts

\[ x^{2y_1-2}_{opt} \]

Here is how we do a sum

\[ \sum_{i=1}^{100} x_i \]

Here is how to write an integral:

\[ \int_{0}^{\infty} dx \exp(-x^2) \]

\[ \int_{0}^{\infty} dx e^{-x^2} \]

\[ f(x,y) = \frac{\sin(xy) }{1 + \exp(x+y) } \]

\[ f(x,y) = x + y^2 \]

\[ \frac{\partial f}{\partial x} = 1 \]

\[ \frac{\partial f}{\partial y} = 2y \]

\[ \nabla f \]

\[ \nabla f = \begin{bmatrix} \frac{\partial f}{\partial x} & \frac{\partial f}{\partial y} \end{bmatrix} ^T \]

\[ \nabla f = \begin{bmatrix} \frac{\partial f}{\partial x} \\ \frac{\partial f}{\partial y} \end{bmatrix} \]

The Identity in 3D

\[ I = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \]